Topic 3.4-4

This topic focuses on building the conceptual understanding that division is related to multiplication. While multiplication is a procedure used to determine a total value when equal groups are combined, division is a procedure that can be used to determine the number of items in each group when a starting amount is shared equally. Because they are inverse operations, multiplication can be used to find unknowns in division problems and division can be used to find unknowns in multiplication.

Common Core

3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned into equal shares of 8 objects each.

Georgia

MGSE3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares (How many in each group?), or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (How many groups can you make?). For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

1. Given an equal shares word problem, with a dividend of 20 or less and a single digit divisor that will result in a quotient without a remainer, the student will create a model and write an equation to correctly solve the problem with at least 90% accuracy by the end of the first marking period.
2. Given a division problem containing a single-digit divisor and visual model, the student will apply an understanding of the inverse relationship of multiplication and division to accurately solve for unknowns for 5 out of 6 examples.
3. Given a division equation, with a dividend of 40 or less and a single digit divisor that will result in a quotient without a remainder, the student will apply previously learned strategies to find the quotient with 90% accuracy for 4 out of 5 trials.

ViewGuided LessonUse division models and equations to solve multiplication problems with unknowns, and use multiplication models and equations to solve division problems with unknowns to see the inverse relationship.(12-18 min)

This topic extends understanding of division to remainders. When sharing equally
there are times in which the quotient results in “leftovers” which are called remainders. Lessons progress from models only with remaining amounts displayed outside the answer bins to numbers only. Because they are inverse operations, multiplication can be used to check the accuracy of division problems with and without the use of models.

Common Core

3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned into equal shares of 8 objects each.

3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations.

Georgia

MGSE3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares (How many in each group?), or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (How many groups can you make?). For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

MGSE3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

MGSE3.OA.6 Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

MGSE3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of one-digit numbers.

1. Given an equal shares word problem with a dividend of 20 or less and a single digit divisor that will result in a quotient with a remainder and visual model, the student will create a model and write an equation to correctly solve the problem for 5 out of 6 examples.
2. Given a division problem containing a single-digit divisor that will result in a quotient with a remainder, the student will apply an understanding of the inverse relationship of multiplication and division to accurately solve for the quotient check their work with at least 90% accuracy by the end of the first marking period.
3. Given a division equation, with a dividend of 50 or less and a single digit divisor that will result in a quotient with a remainder, the student will apply previously learned strategies to find the quotient with 90% accuracy for 4 out of 5 trials.

This topic focuses on building the conceptual understanding of the distributive property, specifically subtracting 1 group from a known fact with factors 5 or 10 to determine the product of an unknown fact with factors 4 or 9. Students work with arrays and number lines to create a model with 5 or 10 groups and then cross out one group to determine the product of the given fact. They represent the model using equations that include parenthesis and partial products.

Common Core

3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5x7 as the total number of objects in 5 groups of 7 objects each.

Georgia

MGSE3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

1. Given a set of 10 multiplication problem for facts containing 4 and 9 and visual models, the student will apply the distributive property to correctly solve for the product for 5 out of 6 examples by the end of the first marking period.
2. Given multiplication equations for facts containing 4 or 9 and previous guided practice using visual models, the students will gain fluency by passing automaticity tests with at least 90% accuracy upon completion of the IEP.

ViewGuided LessonMake two part models and complete equations that contain parenthesis and partial products using the groups sizes of 5 or 10 and a subtraction strategy to find the product of a given fact.(12-18 min)

This topic focuses on the procedural skill of applying the distributive property. Lessons now require students to change either the first or second factor and apply strategies learned in Unit 2 and previously in this unit.

Common Core

3.OA.D.8 Solve two-step problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Georgia

MGSE3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

1. Given a multiplication fact along with visual models, the student will distribute one of the factors to solve for the product with at least 90% accuracy by the end of the second quarter.
2. Given a multiplication fact involving factors of 4 or 9 and vocabulary reinforcement, the student will use the factors 5 or 10 to solve for the product for 5 out of 6 examples upon completion of the IEP.
3. Given a set of 10 multiplication equations for facts and previous guided practice using visual models, the students will gain fluency by passing automaticity tests with at least 90% by the end of the first term.

Multiplication and division are about working with groups of items and are inverse operations. Division can be used to find the size of each group when a starting amount is shared equally.

Common Core

3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5x7 as the total number of objects in 5 groups of 7 objects each.

3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned into equal shares of 8 objects each.

3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × = 40, one knows 40 ÷ 5 = 8) or properties of operations.

3.OA.D.8 Solve two-step problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Georgia

MGSE3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

MGSE3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares (How many in each group?), or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (How many groups can you make?). For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

MGSE3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

MGSE3.OA.6 Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

MGSE3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of one-digit numbers.

MGSE3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.